Advertisements
Advertisements
प्रश्न
In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.
If AD = 4x - 3, AE = 8x - 7, BD = 3x - 1 and CE = 5x - 3,Find x.
उत्तर
In ΔADE and ΔABC
∠D = ∠B and ∠C = ∠E ...(DE || BC)
⇒ ΔADE ∼ ΔABC
∴ `"AD"/"DB" = "AE"/"EC"`
⇒ `(4x - 3)/(3x - 1) = (8x - 7)/(5x - 3)`
⇒ (4x - 3) x (5x - 3) = (8x - 7) x (3x - 1)
⇒ 20x2 - 15x - 12x + 9 = 24x2 - 21x - 8x + 7
⇒ 20x2 - 27x + 9 = 24x2 29x + 7
⇒ 4x2 - 2x - 2 = 0
⇒ `x(x - 1) + (1)/(2)(x - 1)` = 0
⇒ `(x + 1/2)` = 0; x - 1 = 0
⇒ x = `-(1)/(2); x = 1`
∴ x = 1.
APPEARS IN
संबंधित प्रश्न
In the given figure, AB and DE are perpendicular to BC.
1) Prove that ΔABC ∼ ΔDEC
2) If AB = 6 cm; DE = 4 cm and AC = 15 cm. Calculate CD.
3) Find the ratio of area of ΔABC: area of ΔDEC
In the given figure, ABC is a triangle. DE is parallel to BC and `(AD)/(DB) = 3/2`.
- Determine the ratios `(AD)/(AB)` and `(DE)/(BC)`.
- Prove that ∆DEF is similar to ∆CBF. Hence, find `(EF)/(FB).`
- What is the ratio of the areas of ∆DEF and ∆BFC?
In the given figure, ΔODC~ΔOBA, ∠BOC = 115° and ∠CDO = 700.
Find (i) ∠DCO (ii) ∠DCO (iii) ∠OAB (iv) ∠OBA.
A model of a ship is made with a scale factor of 1 : 500. Find
The volume of the ship, if the volume of its model is 200 cm3.
Choose the correct alternative:
If ΔABC ~ ΔPQR and 4A (ΔABC) = 25 A(ΔPQR), then AB : PQ = ?
Find the area of the triangle ABC with the coordinates of A as (1, −4) and the coordinates of the mid-points of sides AB and AC respectively are (2, −1) and (0, −1).
Find the scale factor in each of the following and state the type of size transformation:
Actual area = 64m2, Model area = 100cm2
If figure OPRQ is a square and ∠MLN = 90°. Prove that ∆LOP ~ ∆QMO
D is the mid point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that c2 = `"p"^2 - "a"x + "a"^2/4`
Two triangles are similar. Smaller triangle’s sides are 4 cm, 5 cm, 6 cm. Perimeter of larger triangle is 90 cm then find the sides of larger triangle.
